Abstract: Latin hypercube designs (LHDs) have been applied in
many computer experiments among the space-filling designs found in
the literature. A LHD can be randomly generated but a randomly
chosen LHD may have bad properties and thus act poorly in
estimation and prediction. There is a connection between Latin
squares and orthogonal arrays (OAs). A Latin square of order s
involves an arrangement of s symbols in s rows and s columns, such
that every symbol occurs once in each row and once in each column
and this exists for every non-negative integer s. In this paper, a
computer program was written to construct orthogonal array-based
Latin hypercube designs (OA-LHDs). Orthogonal arrays (OAs) were
constructed from Latin square of order s and the OAs constructed
were afterward used to construct the desired Latin hypercube designs
for three input variables for use in computer experiments. The LHDs
constructed have better space-filling properties and they can be used
in computer experiments that involve only three input factors.
MATLAB 2012a computer package (www.mathworks.com/) was
used for the development of the program that constructs the designs.
Abstract: Let n be an integer. We show the existence of at least
three non-isomorphic non-commutative Latin squares of order n
which are embeddable in groups when n ≥ 5 is odd. By using a
similar construction for the case when n ≥ 4 is even, we show that
certain non-commutative Latin squares of order n are not embeddable
in groups.
Abstract: Quasigroups are algebraic structures closely related to
Latin squares which have many different applications. The
construction of block cipher is based on quasigroup string
transformation. This article describes a block cipher based
Quasigroup of order 256, suitable for fast software encryption of
messages written down in universal ASCII code. The novelty of this
cipher lies on the fact that every time the cipher is invoked a new set
of two randomly generated quasigroups are used which in turn is
used to create a pair of quasigroup of dual operations. The
cryptographic strength of the block cipher is examined by calculation
of the xor-distribution tables. In this approach some algebraic
operations allows quasigroups of huge order to be used without any
requisite to be stored.